[Nerwen]

Short answer: it doesn't fit. Not in itself, anyway.

From memory, though, Tolkien's catch-all explanation for this and other poems included in "Tales from the Perilous Ream", is that they're traditional songs which reflect actual happenings, if at all, only in the distorted way of folklore.

Following that concept, "Firiel" would be some unknown person's idea of how the "sailing into the West" business worked, rather than a true story. You know, just like the "Man in the Moon" poems aren't presented as a factual account of the life and times of Tilion.